In this paper, we present a powerful spectral shape descriptor for shape analysis, named Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). We proposed a novel manifold harmonic signal processing tool termed Anisotropic Spectral Manifold Wavelet Transform (ASMWT) first. ASMWT allows to comprehensively analyse signals from multiple wavelet diffusion directions on local manifold regions of the shape with a series of low‐pass and band‐pass frequency filters in each direction. Based on the ASMWT coefficients of a very simple signal, the ASMWD is efficiently constructed as a localizable and discriminative multi‐scale point descriptor. Since the wavelets used in our descriptor are direction‐sensitive and able to robustly reconstruct the signals with a finite number of scales, it makes our descriptor compact, efficient, and unambiguous under intrinsic symmetry. The extensive experiments demonstrate that our descriptor achieves significantly better performance than the state‐of‐the‐art descriptors and can greatly improve the performance of shape matching methods including both handcrafted and learning‐based methods.
Shape descriptors have recently gained popularity in shape matching, statistical shape modeling, etc. Their discriminative ability and efficiency play a decisive role in these tasks. In this paper, we first propose a novel handcrafted anisotropic spectral descriptor using Chebyshev polynomials, called the anisotropic Chebyshev descriptor (ACD); it can effectively capture shape features in multiple directions. The ACD inherits many good characteristics of spectral descriptors, such as being intrinsic, robust to changes in surface discretization, etc. Furthermore, due to the orthogonality of Chebyshev polynomials, the ACD is compact and can disambiguate intrinsic symmetry since several directions are considered. To improve the ACD’s discrimination ability, we construct a Chebyshev spectral manifold convolutional neural network (CSMCNN) that optimizes the ACD and produces a learned ACD. Our experimental results show that the ACD outperforms existing state-of-the-art handcrafted descriptors. The combination of the ACD and the CSMCNN is better than other state-of-the-art learned descriptors in terms of discrimination, efficiency, and robustness to changes in shape resolution and discretization.
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